- #1
Faust90
- 20
- 0
Hi,
I want to calculate the position-wave-function of a system of two free electrons with momenta k1 and k2 (vectors).
1. Homework Statement
So, I want to have Psi_(k1,k2)(x1,x2) for a state |k1,k2>
I also know that <k'|k> = (2Pi)^3 Delta(k-k')
I tried the following:
Psi(x1,x2)=<x1,x2|k1,k2>=<x1,x2|1|k1,k2>=Integral<x1,x2|k1',k2'><k1',k2'|k1,k2>dk1dk2
The first term <x1,x2|k1',k2'> are the momenta eigenfunction in Space presentation, the second term is the given delta-function:
= Integral Exp(ik1'x1)Exp(ik2'x2) Delta(k1-k1')Delta(k2-k2')
=Exp(ik1x1)Exp(ik2x2)
Is that right?
I'm a bit confused about k1,k2 and k1',k2'Best regards :-)
Faust
I want to calculate the position-wave-function of a system of two free electrons with momenta k1 and k2 (vectors).
1. Homework Statement
So, I want to have Psi_(k1,k2)(x1,x2) for a state |k1,k2>
I also know that <k'|k> = (2Pi)^3 Delta(k-k')
The Attempt at a Solution
I tried the following:
Psi(x1,x2)=<x1,x2|k1,k2>=<x1,x2|1|k1,k2>=Integral<x1,x2|k1',k2'><k1',k2'|k1,k2>dk1dk2
The first term <x1,x2|k1',k2'> are the momenta eigenfunction in Space presentation, the second term is the given delta-function:
= Integral Exp(ik1'x1)Exp(ik2'x2) Delta(k1-k1')Delta(k2-k2')
=Exp(ik1x1)Exp(ik2x2)
Is that right?
I'm a bit confused about k1,k2 and k1',k2'Best regards :-)
Faust